Finite Group Databasebeta

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C2×C49×C125 #72190602

order12250
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C4×C7×C25 (order 4200) · Inn(G) = C1 · Out(G) = C2×C3×C4×C7×C25
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC12250
abelianC2×C49×C125
multiplicative(ℤ/12251)ˣ, (ℤ/24502)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7×C25C2×C5×C7
socle, prime radicalC2×C5×C7C7×C25
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12250 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic12250, D24500
maximal subgroup ofC4×C49×C125, C22×C49×C125, C2×D6125, …
maximal normal subgroup ofC4×C49×C125, C22×C49×C125, C2×D6125, …
maximal quotient ofC4×C49×C125, C22×C49×C125
automorphism group ofC12251
outer automorphism group ofC12251

GAP

Past the SmallGroups library coverage — no SmallGroups id.